Geodesic
The Kodaira dimension of the moduli space of Prym varieties
Journal of the European Mathematical Society, Tome 12 (2010) no. 3, pp. 755-795.

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We study the enumerative geometry of the moduli space Rg​ of Prym varieties of dimension g–1. Our main result is that the compactication of Rg​ is of general type as soon as g>13 and g is different from 15. We achieve this by computing the class of two types of cycles on Rg​: one defined in terms of Koszul cohomology of Prym curves, the other defined in terms of Raynaud theta divisors associated to certain vector bundles on curves. We formulate a Prym–Green conjecture on syzygies of Prym-canonical curves. We also perform a detailed study of the singularities of the Prym moduli space, and show that for g≥4, pluricanonical forms extend to any desingularization of the moduli space.
DOI : 10.4171/jems/214
Classification : 14-XX, 11-XX, 00-XX 
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Gavril Farkas; Katharina Ludwig. The Kodaira dimension of the moduli space of Prym varieties. Journal of the European Mathematical Society, Tome 12 (2010) no. 3, pp. 755-795. doi : 10.4171/jems/214. http://geodesic.mathdoc.fr/articles/10.4171/jems/214/

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